Deriving Snell's Law from an Optimization Problem Refraction is a physical phenomenon that happens when light, or more generally a wave, passes through two different mediums. In this problem, we consider two mediums separated by an horizontal line of length d (for example, this line could separate the water in a pool and the air above it). A photon is emitted from a source placed at a point A and detected at a point B. See Figure 1 for the placement of A and B. First Medium A hi d h2 Second Medium B Figure 1: Photon emission and detection points. The speeds of the photon in the first and second medium are v1 and v2, respectively. The refraction indexes are defined as n1 = y, and n2 = , where c is the speed of light in vacuum. Assuming that the photon travels on the fastest path from A to B, prove Snell's law of refraction sin 01 U1 n2 sin 02 (1) n1 where 61 and 02 are the angles defined in Figure 2